In this paper we establish the existence and uniqueness of the local solutions to the incompressible Euler equations in , , with any given initial data belonging to the critical Besov spaces . Moreover, a blowup criterion is given in terms of the vorticity field.
Dans cet article on établit l’existence et l’unicité de la solution locale de l’équation d’Euler incompressible dans , , avec des données initiales quelconques appartenant aux espaces de Besov critique . De plus, un critère d’explosion est donné en terme du champ de vorticités.
Keywords: well-posedness, Euler equations, Besov spaces
Mot clés : bien-posé, equations d'Euler, espaces de Besov
Zhou, Yong 1
@article{AIF_2004__54_3_773_0, author = {Zhou, Yong}, title = {Local well-posedness for the incompressible {Euler} equations in the critical {Besov} spaces}, journal = {Annales de l'Institut Fourier}, pages = {773--786}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {3}, year = {2004}, doi = {10.5802/aif.2033}, zbl = {1097.35118}, mrnumber = {2097422}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2033/} }
TY - JOUR AU - Zhou, Yong TI - Local well-posedness for the incompressible Euler equations in the critical Besov spaces JO - Annales de l'Institut Fourier PY - 2004 SP - 773 EP - 786 VL - 54 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2033/ DO - 10.5802/aif.2033 LA - en ID - AIF_2004__54_3_773_0 ER -
%0 Journal Article %A Zhou, Yong %T Local well-posedness for the incompressible Euler equations in the critical Besov spaces %J Annales de l'Institut Fourier %D 2004 %P 773-786 %V 54 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2033/ %R 10.5802/aif.2033 %G en %F AIF_2004__54_3_773_0
Zhou, Yong. Local well-posedness for the incompressible Euler equations in the critical Besov spaces. Annales de l'Institut Fourier, Volume 54 (2004) no. 3, pp. 773-786. doi : 10.5802/aif.2033. https://aif.centre-mersenne.org/articles/10.5802/aif.2033/
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